# Properties

 Label 980.1.f Level $980$ Weight $1$ Character orbit 980.f Rep. character $\chi_{980}(99,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $5$ Sturm bound $168$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 980.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(980, [\chi])$$.

Total New Old
Modular forms 24 18 6
Cusp forms 8 8 0
Eisenstein series 16 10 6

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8 q - 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{9} + 8 q^{16} + 4 q^{25} - 4 q^{29} - 4 q^{30} + 4 q^{36} - 4 q^{46} - 4 q^{50} - 4 q^{65} + 8 q^{74} - 4 q^{85} - 4 q^{86} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(980, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
980.1.f.a $$1$$ $$0.489$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$$
980.1.f.b $$1$$ $$0.489$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$1$$ $$1$$ $$0$$ $$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$$
980.1.f.c $$1$$ $$0.489$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$-1$$ $$1$$ $$0$$ $$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$$
980.1.f.d $$1$$ $$0.489$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$-1$$ $$0$$ $$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$$
980.1.f.e $$4$$ $$0.489$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots$$